Expansions of Price Equation for Viability and Fecundity Selection
The Price equation offers a means of separating the portion of population change attributable to natural selection from the overall change. There is debate over the universality of the Price equation due to the belief that it makes simple assumptions. However, it should be noted that the definition of fitness is assumed within the Price equation. To account for populations subject to viability selection and fecundity selection during their life cycle, two expansions of the Price equation have been proposed based on a clear understanding of fitness. These expansions include three terms: a viability selection term, a fecundity selection term, and a mean value term that captures the difference between adults and their zygotes. Unlike the classic Price equation, which also has a mean value term capturing the difference between adults and their successful zygotes, the mean value term in our expansions will be zero in the absence of mutation, drift, and recombination. Furthermore, the individual-based simulation shows that our expansions can outperform the classic Price equation in capturing the average change in strategy for resource allocation. In summary, our expansions fully capture the effects of natural selection and separate them into viability and fecundity selection terms. Our expansions allows for a wider application of the Price equation, especially in the case where there is a trade-off between viability and fecundity selection.